In laminated rocks such as shales, compressional and shear waves propagate with different velocities in different directions. Therefore, when wells are drilled with an angle different from 0 or 90 degrees with respect to the lamination or bedding (i.e. deviated wells), the wave velocities measured along the wells are different from the velocities parallel or perpendicular to the bedding or lamination. In FIG. 1, a deviated well drilled at an angle θ through a laminated medium is illustrated. What actually is measured in this illustration is the velocity along the angle (Vθ). The same situation exists when a vertical or a horizontal well is drilled in a dipping layer with lamination. In either case, the velocity angle (Vθ) is being measured and in order to get vertical velocity (V0) or horizontal velocity (V90) if the well is near horizontal, deviation or anisotropy correction is required. Because sonic log measurements are used in many other applications such as, for example, geo-mechanics, hydraulic fracturing, borehole seismic, and wellbore stability, such corrections are crucial.
There are a limited number of published techniques for deviation correction; however, such techniques are not often practiced in the logging industry. Also such techniques, if practiced, may require advanced logging suites such as dipole sonic compared to the less expensive monopole sonic. And, some of these techniques are interval based methods-meaning they assume that each interval (lithological layer) has constant anisotropy parameters that are not the case in real earth. Some of these techniques also assume a group velocity is being measured instead of the more preferred phase velocities. Nevertheless, such techniques do not correct the effects of dispersion on sonic log measurements of deviated wells in laminated formations.
In order to validate the corrected sonic log measurements, conventional techniques may require sonic log measurements from vertical or near vertical wells that are close to the location of the deviated well where the correction is being applied. Even assuming sonic log measurements from neighboring wells are available, the process of validating the corrected sonic log measurements can be expensive. Conventional techniques thus, are not often practiced in the logging industry and mechanical properties that are interpreted from sonic log measurements can be inaccurate.